2012×2013+2011= 4050156+201=4052167

2014×2013-2015=4054182-2015=4052167

2012 x 2013 + 2011 = 4050156 + 2011 = 4052167
2014 x 2013 - 2015 = 4054182 - 2015 = 4052167
HOK TỐT

2012x2013+2011=4050156+2011=4052167

2014x2013-2015=4054182-2015=4052167

           chúc học tốt !!!

\(A=\left|x-2011\right|+\left|x-2012\right|+\left|x-2013\right|+\left|x-2014\right|+\left|x-2015\right|\)

\(=\left(\left|x-2011\right|+\left|x-2015\right|\right)+\left(\left|x-2012\right|+\left|x-2014\right|\right)+\left|x-2013\right|\)

Đặt \(B=\left|x-2011\right|+\left|x-2015\right|\)

\(=\left|x-2011\right|+\left|2015-x\right|\ge\left|x-2011+2015-x\right|=4\left(1\right)\)

Dấu"=" xảy ra \(\Leftrightarrow\left(x-2011\right)\left(2015-x\right)\ge0\)

\(\Leftrightarrow\hept{\begin{cases}x-2011\ge0\\2015-x\ge0\end{cases}}\)hoặc \(\hept{\begin{cases}x-2011< 0\\2015-x< 0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}x\ge2011\\x\le2015\end{cases}}\)hoặc \(\hept{\begin{cases}x< 2011\\x>2015\end{cases}\left(loai\right)}\)

\(\Leftrightarrow2011\le x\le2015\)

Đặt \(C=\left|x-2012\right|+\left|x-2014\right|\)

\(=\left|x-2012\right|+\left|2014-x\right|\ge\left|x-2012+2014-x\right|=2\left(2\right)\)

Dấu"="xảy ra \(\Leftrightarrow\left(x-2012\right)\left(2014-x\right)\ge0\)

\(\Leftrightarrow\hept{\begin{cases}x-2012\ge0\\2014-x\ge0\end{cases}}\)hoặc \(\hept{\begin{cases}x-2012< 0\\2014-x< 0\end{cases}}\) 

\(\Leftrightarrow\hept{\begin{cases}x\ge2012\\x\le2014\end{cases}}\)hoặc\(\hept{\begin{cases}x< 2012\\x>2014\end{cases}\left(loai\right)}\)

\(\Leftrightarrow2012\le x\le2014\)

Ta có: \(\left|x-2013\right|\ge0;\forall x\left(3\right)\)

Dấu"="Xảy ra \(\Leftrightarrow\left|x-2013\right|=0\)

                      \(\Leftrightarrow x=2013\)

Từ (1),(2) và (3) \(\Rightarrow B+C+\left|x-2013\right|\ge6\)

Hay \(A\ge6\)

Dấu"="xảy ra \(\Leftrightarrow\hept{\begin{cases}2011\le x\le2015\\2012\le x\le2014\\x=2013\end{cases}}\)\(\Leftrightarrow x=2013\)

Vậy \(A_{min}=6\Leftrightarrow x=2013\)

$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$

$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$

$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$

$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$

$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$

dễ ợt nhưng éo biết làm thông cảm nha

ban Dang Ha Trang an noi gi ki vay 

\(\Rightarrow x^{2014}+y^{2014}-2\left(x^{2013}+y^{2013}\right)+x^{2012}+y^{2012}=0\)

\(\Leftrightarrow x^{2012}.\left(x-1\right)^2+y^{2012}.\left(y-1\right)^2=0\)

\(\Rightarrow x=1;y=1\)

\(\Rightarrow P=2\)

cai gi

hgjkgj

Giá trị biểu thức 2012 x 2013+2011/2014x2013 -2015

Giá trị biểu thức 2012 x 2013+2011/2014x2013 -2015

Giá trị biểu thức 2012 x 2013+2011/2014x2013 -2015

Giá trị biểu thức 2012 x 

Giá trị biểu thức 2012 x 2013+2011/2014x2013 -2015

ai h minh h lai 2013+2011/2014x2013 -2015